Risk of Ruin

A few weeks ago we received an email advertising a tipster with the title ‘Exploding the Myth: Making Money from 1/4 Shots’. Before I go further this is not an inspection of the tipster but is simply using this example as an examination of the logic that this third party goes on to use in his recommended staking plan, and will hopefully give you a better idea of how you should think about your staking and why.


Our advertiser initially starts with a statement that he is looking to disprove, that “you can’t make a profit backing short priced favourites”. He is right to state this is false of course – if you are good at finding value at 1.25 shots then you will be successful, as you will be if you are good at finding over-priced bets at any price. The downside of short-priced betting is simply that there is a clear limit on the maximum value you are going to be able to find. With a longer priced bet you may in some circumstances believe there is a value of over 20% in the price offered, while with a 1.25 shot 20% value would imply that a bet is guaranteed to win – the bookies sometimes get things wrong but rarely that wrong!

Now, and this is his big selling point, he goes on to say that using level stakes he suggests using a bank of just 15 points (thereby allowing you to roll over you bank more often and therefore increase your profits. So is he right? And what is the maths behind this decision?


Example

Our tipster had past results showing a 2.7% edge from 611 bets so we’ll use these figures. To start assume we have a bank of 100 units, we have our edge, but are placing bets at 2.00 (i.e. double or nothing on each bet), and we are going to risk one unit per bet over 1000 bets. In this scenario the chance of going bust is just 0.45% so the risk of ruin (RoR) is very small indeed. However, if our bank was just 15 units then our risk of going bust increases to 44.5% and suddenly there is a very real chance of us losing the lot.

The real danger here though is not so much in our staking but in our initial assumption that we have a 2.7% edge (this is probably the most common mistake by punters), and is one of the biggest reasons to avoid over-staking. Hopefully sensible staking allows you to build a bank but also gives greater confidence in your past results and if you discover they weren’t as good as they initially looked will also give you time to stop/make adjustments before you go bust.

The confidence intervals surrounding historic results are much larger than you would probably think and depending on the number of results in the sample, that edge could easily be ±10% of your mark. In this case, if we assume there was a standard deviation of one for the sample, we have a 90% confidence interval of ±7% from our +2.7% figure. If the real edge was actually just 1% then our 100 unit bank would go bust 13.5% of the time – still acceptable – but a 15 unit bank would go bust a huge 74.1% of the time.

But this strategy involves placing bets at 1.25 and not 2.00 – so there’s no chance of that happening here is there… surely?

Well the standard deviation would be closer to 0.50 which would give us a smaller band for our confidence interval, which would now be more like ±3.3% from the observed +2.7%. This fact means that our advertiser was correct in that you can afford to increase stakes if you find value for shorter priced bets as we are more confident in our observed edge. Our RoR with a 15 unit bank is now just 11.9% assuming the 2.7% edge is correct.  However, if the real edge is actually only 1% then our RoR increases to 46.6% and so while a 15 unit bank might look a fair choice given the shorter odds it’s probably too risky given a small change in our edge could be very costly. Instead a 25 unit bank would be far more appropriate as the RoR would be just 2.9% if our edge is correct and a more reasonable 28.0% in the scenario of just a 1% edge.


Conclusion

So the questions to ask yourself when you are deciding your stakes is: how big is your bank, how confident are you in your past results (which should be based on success and sample size), and what is your propensity towards risk (are you risk-averse or risk-loving and what level of RoR are you willing to tolerate?). You will often look at historic results and decide that you’d have made more money by level staking all your bets, including those at long odds-against as well as those at short odds-on but it’s important to remember that while theoretically you might make more with that strategy your RoR also increases and you may go bust before those large returns ever materialise.

Once you have assessed these factors you will have a better idea of what you are willing to stake on each bet and then you simply need the discipline to stick to it. Generally speaking though, a variable staking plan that returns you about 1-2% of your bank per bet is appropriate for most users.


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